The previously unseen photo shows the two-year-old royal feeding the chickens while wearing Peppa Pig wellies, stone-washed jeans and a grey long-sleeved top.
The duchess shared the family photo as part of her appearance on the Ellen show, where she also revealed that the youngster dressed as a dinosaur for Halloween.
“It’s so sweet, he’s so sweet with the chickens too,” said DeGeneres who is Meghan’s neighbour.
“Archie is such a gentle soul, he really is.”
The duchess said she had no regrets after quitting royal life, revealing that husband Harry “loves” life in the US. “We’re just happy,” she said.
The couple relocated to the US after stepping back as senior royals early last year.
Meghan also told DeGeneres that she and Prince Harry went to a post-apocalypse themed Halloween party disguised in costumes before the world knew they were a couple.
They were joined by Princess Eugenie and her now husband Jack Brooksbank.
“The four of us snuck out in Halloween costumes to just have one fun night on the town before it was out in the world that we were a couple,” Meghan said.
During the interview, the duchess also talked about how five-month old daughter Lilibet was teething, to which DeGeneres jokingly suggested tequila.
Meghan replied: “That’s Auntie Ellen for you.”
The broadcast comes eight months after the couple were interviewed by Oprah Winfrey in a bombshell TV special.